Quantum Mechanics 390-FS2-1MKD

Quantum Mechanics is the one semestral course of the subject. It includes 30 hours of the lecture and 30 hours of the discussion session (2 hours of the lecture and 2 hours of the discussion session per a week).

Educational profile: general academic.

Type of the studies: full-time.

Block (unit): theoretical physics, mandatory subject.

Field of knowledge and discipline of science: physical science, quantum mechanics.

Year of the studies, semester: 1st year, 1st semester, graduate studies.

Introductory conditions: course of analysis, course of algebra, course of classical mechanics, elements of classical electrodynamics, elements of
quantum mechnics

Didactic methods: lecture, solving the problems, homework, discussions, consultations, unassisted studying.

ECTS points: 9.

Balance sheet of the student's work: lecture (45 hours), discussion session (45 hours), homework (90 hours), discussions (5 hours), consultations (15 hours), unassisted studying (90 hours).

Quantitative indicators: lecture (2 ECTS points), discussion session (2 ECTS points), homework (2 ECTS points), discussions (0,5 ECTS points), consultations (0,5 ECTS points), unassisted studying (2 ECTS points).

The content is following:

Finite-dimensional quantum mechanics.
Bloch sphere.
Quantum states as vectors in Hilbert space.
Quantum states as operators.
Time evolution.
Observables and mixed states.
States of subsystems.
No-cloning and no-deleting theorems, quantum teleportation, superdense coding, quantum non-demolition measurements, quantum computers.
Quantum models on the Hilbert space.
Interpretations of quantum mechanics.
Quantization, the quantum harmonic oscillator.
Perturbation calculation for the time independent non-relativistic Schrödinger equation.
Calculus of variations applied to determine the energy levels of the ground state.
Pauli exclusion principle.
Time-depandent perturbation theory for the Schrödinger equation.
Transitions between levels for the 2-level system.
Pauli equation for a spin- ½ particle.
Zeeman effect.
Stark effect in an electric field.

Type of course

Mode

(in Polish) w sali

Requirements

Algebra
Analysis I
Analysis II
Elements of Classical Electrodynamics
Elements of Quantum Mechanics
Elements of Theoretical Mechanics

Prerequisites

Algebra
Analysis I
Analysis II
Elements of Classical Electrodynamics
Elements of Quantum Mechanics
Elements of Theoretical Mechanics

Prerequisites (description)

The main goal of the subject is to apply quantum mechanics to explain those physical phenomena, which otherwise remain outside the scope of classical physics. Specially one needs to learn and use Dirac's notation for describing expressions, which are very difficult to handle in their full explicit mathematical form. The relevance of various symmetries of the analyzed systems are discussed. The perturbation methods show the reality of practical quantum mechanical computations for physical systems.

Course coordinators

Edward Piotrowski

Learning outcomes

A student:

1. She/he understands the role of physical theory and abstract description of physical objects and physical phenomena in the scope of selected issues of contemporary physics and its applications.

2. She/he has an extended knowledge of selected sections of theoretical physics, knows and understands basic theoretical concepts and mathematical models of selected systems and phenomena.

3. She/he is able to popularly quote contemporary achievements in the field of known branches of physics, present the latest practical solutions based on scientific research.

4. She/he knows how to apply theoretical physics methods to quantitative and qualitative analysis of selected systems and physical phenomena within the scope of the specialization program.

5. She/he is able to understand and critically use professional literature and Internet resources - including sources in English in relation to the studied physics problems.

Codes: K_W02, K_W09, K_U01, K_U09, K_U10.

Assessment criteria

Students take part in lectures broaden of computer simulations, illustrating transmitted contents. They are stimulated for asking the questions and for discussion.

Written and oral examinations undergo after the end of the course of Quantum Mechanics. They verify acquirement of knowledge.

Students get the series of questions, exercises and problems for individual and unassisted solving. During the course, students present solutions of given problems. Lecturer is advised to pay close attention to understanding used concepts and clarity of presentations. He stimulates students group for asking the questions and discussions. Lecturer tries to create sense of responsibility for team inside the students group and he encourages the group to join work.

Assessment of student learning is based on the grade, which includes:

1. Ability to solve the problems from define parts of quantum mechanics.

2. Ability to present the solutions.

3. Ability to discuss subjects and problems of the course.

4. Ability to use the literature and Internet sources.

5. Ability to collaborate inside the team.

6. Creative approach to solved problems.

Permanent grading by lecturer.

Final grade is expressed by the number established in the study regulation, which includes evaluation of the knowledge, abilities and competencies of the student.

Bibliography

1) L. I. Schiff: "Quantum mechanics"

2) I. Białynicki-Birula, M. Cieplak, J. Kamiński: "Theory of Quanta"

3) D.J. Griffiths; "Introduction to quantum mechanics".

4) M. Hirvensalo. "Quantum Computing"

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 390-FS2-1MKD in USOSweb